A spectacular exhibition of the greatest treasures of one of the most famous libraries in the world features a monument to past folly: a large battered leather volume the Bodleian Library in Oxford sold off as surplus to requirements in 1664 and had to raise a fortune to buy back almost 250 years later.

Now, rather than getting rid of the exhibits, it is holding them in storage. Visitors to the Bodleian's new exhibition, will be invited to suggest which ones deserve to be given permanent display in the new gallery.

The £78m transformation of the New Bodleian will give the library climate-controlled stores and reading rooms, and a museum-quality gallery for the first time.

But few outsiders have any idea of how extraordinary its contents are.

They include Magna Carta; a pristine Gutenberg Bible; a dazzling 14th-century travels of Marco Polo; Philip Pullman; William Blake; Jane Austen's handwritten compendium of her own earliest writings; a 13th-century bestiary showing an elephant being strangled by the only animal it fears, a serpent like dragon; the Codex Mendoza, an account made for the first Spanish viceroy of the Aztec civilisation Spain was destroying; Mary Shelley's draft of Frankenstein with suggestions scribbled in by Shelley; and the earliest almost complete copy of a poem by Sappho, from a cache of extraordinary documents found in a rubbish dump in Egypt in the 19th century.

Curator Stephen Hebron asked every member of staff in the Bodleian for their favourite, then reduced by half the 150 books, maps, letters and documents they regarded as unmissable, with some dating back more than 2,000 years.

Some are in for their content, some for their beauty: one is both hideous and illegible, but Hebron has included it because it is so extraordinary: three charred scrolls from a library in Herculaneum buried by the eruption of Vesuvius which also destroyed Pompeii, presented by George IV.

"It shows that the concept of what we regard as treasure can change dramatically over the years," he said.

"We have documents that we now regard as priceless which were just scraps of paper when they came in. The Shakespeare was in the category which our founder, Bodley, described as 'idle books and riff-raffs'."

The library had the first collection of Shakespeare's plays, gathered by his friends from tattered actors' copies and published seven years after his death, as loose-leaf pages straight from the printers. Bound in plain brown leather, it was among the chained books of Duke Humfrey's Library, part of the Bodleian.

However by 1664 it acquired the Third Folio – much smarter but with six plays now regarded as not Shakespeare – and got rid of the tatty First. It vanished for centuries into private collections, and then in the late 19th century a man brought it in to the Bodleian for identification, when it was recognised by a young librarian.

The library had to raise £3,000 to buy back the Shakespeare First Folio it had so casually disposed of. Last year another copy made £2.8m at auction.

"It was a staggering sum of money for the library to have to raise," Hebron said. "The most they'd ever paid for a book until then was a few hundred pounds. It was a very expensive lesson."

Hebron mourns everything he had to leave out, including the only poem in John Donne's handwriting – "not his best, but still …" – and the Audubon Birds of America, printed on pages so huge the size is known as double elephant. A copy set a new world record for any book last year at £7m.

"This exhibition is teaching us things," Hebron said. "We now know we need a double elephant-sized display case in the new gallery."